Dynamics of a quantum phase transition and relaxation to a steady state

Abstract

We review recent theoretical work on two closely related issues: excitation of an isolated quantum condensed matter system driven adiabatically across a continuous quantum phase transition or a gapless phase, and apparent relaxation of an excited system after a sudden quench of a parameter in its Hamiltonian. Accordingly the review is divided into two parts. The first part revolves around a quantum version of the Kibble-Zurek mechanism including also phenomena that go beyond this simple paradigm. What they have in common is that excitation of a gapless many-body system scales with a power of the driving rate. The second part attempts a systematic presentation of recent results and conjectures on apparent relaxation of a pure state of an isolated quantum many-body system after its excitation by a sudden quench. This research is motivated in part by recent experimental developments in the physics of ultracold atoms with potential applications in the adiabatic quantum state preparation and quantum computation.

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

“…Finally, we believe that our results point the way to future explorations of quantum many-body spin systems, including thermalization and ergodicity crossing a quantum phase transition 34,35 , investigations of Hamiltonian monodromy 28 and other non-linear phenomena, finite temperature effects and dynamic stability. The combination of an exactly solvable Hamiltonian with a quantum phase transition together with demonstrated dynamics in the quantum regime should provide unique insights to these important topics.…”

Kibble-Zurek scaling in holographic quantum quench: backreaction

“…This is particularly so for strongly coupled systems. Nevertheless, Kibble-Zurek scaling has been verified by explicit calculations in many models and is now being seen experimentally as well [3][4][5][6]. 2 In [15] a study of this problem in strongly coupled field theories which have gravity duals via AdS/CFT was initiated and continued in [16] and [17].…”

“…Many years ago, Kibble [1], and subsequently Zurek [2], argued that observables like defect density indeed show scaling behavior. These arguments -which were first developed for thermal quench and recently generalized to quantum quench 1 [7] -imply that for a driving involving a single relevant operator, the time dependence of the one point function of an operator O with conformal dimension x is of the form [4] O(t, v) ∼ v where v is the rate of change of the coupling, ν is the correlation length exponent and z is the dynamical critical exponent. The arguments which lead to (1.1) involve (i) an assumption that once adiabaticity breaks the system evolve in a diabatic fashion and (ii) in the critical region the instantaneous correlation length is the only length scale in the problem.…”

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

“…This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3]. Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep.…”

“…Cold-atom experiments in the past decade have explored a wide variety of non-equilibrium quantum dynamics in previously inaccessible regimes [1,2]. This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3].…”